欧拉旋转定理的另一种证明
An alternative proof for Euler rotation theorem
摘要：
欧拉旋转定理指出，刚体的任何重新配置与其一个点固定等价于绕通过不动点的轴的单次旋转。该定理形成的基础上Chasles'定理指出，它总是可以代表一般位移的刚体的平移和旋转轴。虽然有许多方法可以实现这一点，但旋转轴的方向和旋转旋转角与平移矢量无关。该定理在刚体动力学研究中具有重要意义。这些定理有各种各样的证明，既有几何的也有代数的。本文给出了欧拉旋转定理的一种新的几何证明，它利用绕两个相互垂直的轴的两次连续旋转，从刚体的一个构形到另一个构形，其中一个点固定。
英文摘要：
Euler's rotation theorem states that any reconfiguration of a rigid body with one of its points fixed is equivalent to a single rotation about an axis passing through the fixed point. The theorem forms the basis for Chasles' theorem which states that it is always possible to represent the general displacement of a rigid body by a translation and a rotation about an axis. Though there are many ways to achieve this, the direction of the rotation axis and angle of rotation are independent of the translation vector. The theorem is important in the study of rigid body dynamics. There are various proofs available for these theorems, both geometric and algebraic. A novel geometric proof of Euler rotation theorem is presented here which makes use of two successive rotations about two mutually perpendicular axis to go from one configuration of the rigid body to the other with one of its points fixed.
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